Question: Solve for $x$ and $y$ using elimination. ${-2x+3y = 17}$ ${2x+5y = 55}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2x$ and $2x$ cancel out. $8y = 72$ $\dfrac{8y}{{8}} = \dfrac{72}{{8}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-2x+3y = 17}\thinspace$ to find $x$ ${-2x + 3}{(9)}{= 17}$ $-2x+27 = 17$ $-2x+27{-27} = 17{-27}$ $-2x = -10$ $\dfrac{-2x}{{-2}} = \dfrac{-10}{{-2}}$ ${x = 5}$ You can also plug ${y = 9}$ into $\thinspace {2x+5y = 55}\thinspace$ and get the same answer for $x$ : ${2x + 5}{(9)}{= 55}$ ${x = 5}$